SPE-182605-MS

Coupled Reservoir-Geomechanical Simulation of Caprock Failure and FaultReactivation During CO2 Sequestration in Deep Saline Aquifers

P. H. Winterfeld and Yu-Shu Wu, Colorado School of Mines

Copyright 2017, Society of Petroleum Engineers

This paper was prepared for presentation at the SPE Reservoir Simulation Conference held in Montgomery, TX, USA, 20–22 February 2017.

This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contentsof the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflectany position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the writtenconsent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations maynot be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

AbstractAn aquifer suitable for underground carbon dioxide sequestration needs to be overlain by sealing caprockbecause carbon dioxide is less dense than the native brine and would tend to rise upward. This paper presentsa thermal-hydrological-mechanical (THM) reservoir simulator that is applicable to assessing the sealingcapability of such caprock. The geomechanical portion consists of an equation for mean stress, derivedfrom linear elastic theory for a thermo-poro-elastic system, and equations for stress tensor componentsthat depend on mean stress and other variables. The fluid and heat flow portion of our simulator is forgeneral multiphase, multicomponent, multi-porosity systems. We add the capability of simulating caprockfailure scenarios, namely tensile failure, fracture and fault reactivation, and shear failure, to the formulation.We then show simulation examples for code verification and demonstration of its capabilities, including asimulation of caprock leakage from carbon dioxide injection, a demonstration of the simulator's ability topredict of shear failure, and a simulation an experiment of pressure-induced fracturing of a concrete blockthat includes tensile failure.

IntroductionA promising option for reducing atmospheric anthropogenic carbon dioxide is to inject it undergroundinto a deep saline aquifer. Although this carbon dioxide would be a super critical fluid when injected,it is still less dense than the native brine and would tend to rise upward. Thus, an aquifer suitable forunderground carbon dioxide sequestration needs to be overlain by sealing caprock for the duration ofthe carbon sequestering process. A homogeneous caprock layer with a sufficiently small permeabilitywould inhibit sequestered carbon dioxide from leaking through. However, geological systems often areheterogeneous and discontinuous, and may contain fractures and faults. Carbon dioxide injection pressurizesthe reservoir, and this pressurization can reactivate existing faults and fractures and provide flow paths thatallow leakage of carbon dioxide from the saline aquifer. In addition, if the pressurization is sufficiently high,the caprock can fracture.

A simulation model that can predict caprock failure and fault reactivation would be a useful toolin enhancing our ability to predict reservoir conditions, integrity, and enhance the performance of lifecycle storage operations for carbon dioxide geologic storage. Such a model would couple fluid flow with

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geomechanics, as well as have criteria for caprock failure and fault reactivation. Examples of coupledfluid flow-geomechanical simulators that have been reported in the literature are TOUGH2-FLAC3D(Rutqvist et al., 2002), a linkage of TOUGH2, a well-established code for geohydrological analysis withmultiphase, multicomponent fluid flow and heat transport, and FLAC3D, a widely used commercial codethat is designed for rock and soil mechanics with thermomechanical and hydromechanical interactions;TOUGH–RDCA (Pan et al., 2014), a linkage of TOUGH2 and RDCA, developed for simulating thenonlinear and discontinuous geomechanical behavior of rock; CODE-BRIGHT (Olivella et al., 1996), afinite element code that simulates non-isothermal multiphase flow of brine and gas in deformable media;Code_Aster (Sayedi at al., 2009), a thermal-mechanical finite element code that was coupled to TOUGH2 tosimulate thermo-hydro-mechanical processes under multiphase flow; FEHM (Bower and Zyvoloski, 1997),a coupled thermal-hydrologic-mechanical dual porosity finite element code that allows permeability of upto two perpendicular fracture planes vary with normal stress; and OpenGeoSys (Wang and Kolditz, 2007;Goerke et al., 2011), an object oriented open source thermal-hydrological-mechanical finite element code.

In this paper, we present a thermal-hydrologic-mechanical (THM) simulation model that can predictcaprock failure and fault reactivation. A fully coupled THM simulator was presented by Winterfeld andWu (2014) and Hu et al. (2013). In their approach, the geomechanical equations relating stresses anddisplacements were combined to yield an equation for mean stress, a primary variable, and volumetricstrain, a rock property. This formulation was then extended by Winterfeld and Wu (2016) to calculate thestress tensor components efficiently and is the geomechanical formulation for our simulator. We begin bysummarizing this geomechanical formulation, along with the associated fluid and heat flow formulation, andthen present the formulation used to predict caprock failure and fault reactivation. Example problems arethen used to provide verification of our technique, including a simulation of caprock leakage from carbondioxide injection that is from the literature, a demonstration of the simulator's ability to predict of shearfailure, and a simulation of an experiment of pressure-induced fracturing of a concrete block.

Simulator Fluid Flow and Geomechanical FormulationOur simulator's geomechanical and fluid flow formulation has been described in detail in Winterfeld and Wu(2016) and is outlined here. The fluid flow formulation is based on the TOUGH2 one (Pruess et al., 1999) forgeneral multiphase, multicomponent, multi-porosity systems. Fluid advection is described with a multiphaseversion of Darcy's law. Heat flow occurs by conduction and convection, the latter including sensible as wellas latent heat effects. The description of thermodynamic conditions is based on the assumption of localequilibrium of all phases and rock media.

Our simulator's mean stress geomechanical formulation is based on the classical theory of elasticityextended to multi-porosity non-isothermal media (Winterfeld and Wu, 2014). Hooke's law for such amedium is given by:

(1)

where G is shear modulus, λ is the Lamé parameter, the summation is over multi-porosity continua, α isBiot's coefficient, Tref is reference temperature for a thermally unstrained state, β is linear thermal expansioncoefficient, K is bulk modulus, and ω is porous continuum volume fraction.

Two other fundamental relations in the theory of linear elasticity are the relation between the strain tensorand the displacement vector u:

(2)

and the static equilibrium equation:

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(3)

where Fb is the body force. We combine Equations 1-3 to obtain the thermo-multi-poroelastic Navierequation:

(4)

We then take the divergence of Equation 4 to yield an equation relating mean stress, pore pressures, andtemperatures (Winterfeld and Wu, 2014):

(5)

where τm is mean stress and υ is Poisson's ratio. In addition, the trace of the stress tensor is an invariant andyields a relation between volumetric strain and mean stress, pore pressures, and temperatures:

(6)

where εv is volumetric strain. We couple fluid and heat flow to geomechanics by solving Equation 5 alongwith the mass and energy conservation equations arising from the fluid and heat flow formulation, withmean stress as an additional primary variable and volumetric strain as an additional property.

We calculate stress tensor components after solving for mean stress, pressures, temperatures, and massfractions. The normal stress tensor component in the k-direction, xk, is obtained by taking the k-directionderivative of component k of Equation 4:

(7)

where

(8)

The shear stress tensor component in the k- and l-directions is obtained by averaging the k-directionderivative of component l of Equation 4 and the l-direction derivative of component k of Equation 4:

(9)

The fluid and heat flow and geomechanical equations are discretized in space on a Cartesian grid andsolved using the integral finite difference method (Narasimhan and Witherspoon, 1976). Conservation ofmass, energy, and the mean stress equation are solved simultaneously first. Normal and shear stressesappearing in those equations are evaluated at the previous time step and the rest of the primary variablesare evaluated at the current time step. The normal and shear stress equations are solved next. Normal andshear stresses that do not appear in the Laplacian terms are evaluated at the previous time step, and all otherinstances of primary variables are evaluated at the current time step.

Our simulator is massively parallel, with domain partitioning using the METIS and ParMETISpackages (Karypsis and Kumar, 1998; Karypsis and Kumar, 1999). Each processor computes Jacobianmatrix elements for its own grid blocks and exchange of information between processors uses MPI(Message Passing Interface) and allows calculation of Jacobian matrix elements associated with inter-blockconnections across domain partition boundaries. The Jacobian matrix is solved in parallel using an iterativelinear solver from the Aztec package (Tuminaro et al. 1999).

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Caprock Failure ScenariosIn this section, caprock failure scenarios that are incorporated into our simulator are described. There arethree, with the first being tensile failure of caprock from excess pressurization, the second fault reactivation,and the third shear failure of a fault or caprock.

Tensile FailureCaprock can undergo tensile failure when pressurization from CO2 injection becomes too large. A commonassumption (for example, Chin et al. (2009) and Rutqvist et al. (2008)) is that tensile failure could occurwhen the fluid pressure exceeds the least compressive principal stress. Such an assumption, a conservativeone, is based on the notion that the grain-grain interfaces in the caprock have negligible tensile strengthand those interfaces will break as soon as the effective stress, the difference between the directional appliedstress and the pore pressure, in one direction becomes zero. In our simulator, we include a more generalcaprock tensile failure criterion that allows for non-zero the tensile strength:

(10)

where σm is tensile strength and where σ3 is the least compressive principal stress. We apply Equation10 to each grid block. When Equation 10 becomes satisfied, we then conceptualize the initialization ofa single uniform fracture, perpendicular to the minimum principle stress direction, in the grid block. Weestimate the width of this fracture using a simple model, based on the two-dimensional Perkins-Kern (1961)fracture model, and used by Goodarzi et al. (2012) and Settari and Warren (1994) to couple dynamic fracturepropagation to fluid flow and geomechanics:

(11)

where E is Young's modulus, v is Poisson's ration, hfr is the fracture half height, wfr is the fracture width.The initialization of this fracture modifies the grid block permeability and porosity. We model porosity bylumping the pore volume associated with the newly initialized fracture with the pore volume of the rest ofthe grid block (the grid block matrix) to yield an overall effective porosity:

(12)

where Afr is the fracture face area and m refers to the grid block matrix. We model permeability byconceptualizing flow as occurring through both the fracture and the grid block matrix. For flow orthogonalto the principle minimum stress direction, we average the fracture and grid block matrix permeabilites inseries with cross sectional area weighting:

(13)

where k, l, and j each refer to a Cartesian direction, Δx is grid block length, and Δxlj is the height of the fracturewhen projected into the lj-face. Permeability is unchanged for flow along the principle minimum stressdirection, since fracture permeability is assumed to be much greater than the grid block matrix permeability.Fracture permeability is obtained from the well known expression for laminar flow through a slit:

(14)

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Continued injection of fluid would cause the fracture width to increase and the fracture to extend. Weallow fractures to extend into neighboring grid blocks that do not contain one. We track the fracture frontposition for connections between a grid block that contains a fracture and its neighbors that are in thedirection a fracture would propagate, i.e. the perpendicular to the minimum stress direction. When this frontencompasses the neighboring grid block, a fracture is initiated there. The criterion for the movement of afracture front is given by Mastrojannis et al. (1980), who correlated the velocity of the extending fracturefront as:

(15)

where C and n are parameters that depend on the medium, KIC is rock toughness, and KI is stress intensityfactor at the fracture tip. Yew (2015) gives an expression for this stress intensity factor:

(16)

where r is distance from the fracture front. We evaluate stress intensity factor using the fracture widthcalculated from Equation 11 and the grid block half dimension along the direction of fracture frontpropagation as the distance r from the fracture front.

Fault and Fracture ReactivationFaults are complex systems consisting of a relatively thin inner core zone that has low permeability,surrounded by a fractured damage zone (Wibberly et al., 2009). Injection into a reservoir containing faultswould alter the stress and pressure fields and can change the flow properties of a fault, such as increasing itsability to transmit fluid (reactivation). We approximate the faulted or fractured caprock region as consistingof a network of fractures that may be randomly oriented or have a preferred direction. The permeabilityand porosity of this region can change with changes in the stress and pressure fields, and we generalizethese dependences as:

(17)

and

(18)

where subscript j refers to a Cartesian direction (j=1,2, or 3). One instance of such dependence is fromRutqvist et al. (2002), which conceptualized the fractured medium as an array of cubic blocks with thefractures being the interfaces between them. These fractures are equally spaced and oriented normal toeach Cartesian direction. A fracture aperture is associated with each interface and correlations for fractureporosity and permeability were based on those apertures:

(19)

and

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(20)

where bi is fracture aperture in direction i, kj is permeability in direction j, and subscript 0 refers to a referencecondition where permeability, porosity, and fracture aperture are specified. The dependence on aperturecubed in the permeability correlation results from the representation of flow through the fractures as thatthrough a thin slit.

Fracture aperture is correlated with normal effective stress according to:

(21)

where subscript r refers to a high effective stress residual aperture, subscript max refers to the maximumaperture increase at zero normal effective stress, and d is a parameter.

Shear FailureFaults or weak zones in caprock can undergo shear failure when the shear stress acting on a caprock planeplane exceeds its shear strength. The most common shear failure criterion is the Coulomb (1773) one. Shearfailure is likened to a sliding mass on a plane. The forces acting on the mass are friction, which resistssliding, and is given by its weight multiplied by a factor, and a force exerted on the mass in the direction ofthe plane that causes it to slide. For the Coulomb criteria, the sliding force is the shear stress on the caprockplane, the frictional force is the normal stress on the caprock plane, and an additional term is added thatrepresents the cohesive strength of the material. In addition, when applied to poroelastic media, the normalstress is relaced by the effective normal stress (Terzaghi, 1936):

(22)

where C0 is the cohesion and μ is the coefficient of internal friction. If the orientation of the caprock planeis specified, such as when considering a fault with a given orientation, the stress acting on that plane can beobtained by taking the dot product of the effective stress tensor with that plane's normal vector. That stresshas components normal to that plane (the normal effective stress in Equation 22) and along that plane (theshear stress in Equation 22). For cases in which there is no specified plane, for example caprock containingrandomly oriented fractures, shear failure would occur when the shear and effective normal stresses actingon any plane in the caprock satisfies Equation 22. These effective normal and shear stresses are obtainedfrom the well known Mohr circle (Jaeger et al., 2007), which in equation form is:

(23)

and

(24)

where subscript 1 refers to the maximum principal stress, subscript 3 refers to the minimum principalstress, and θ is the angle measured from the first principal stress direction. Shear failure can be representedgraphically as the intersection of the Mohr circle (Equations 23 and 24) with the Coulomb criterion, Equation22, shown in Figure 1.

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Figure 1—Mohr-Coulomb failure diagram in shear stress-normal effective stress space, with the Mohr circlecentered at point "C" and failure line tangent to Mohr circle at point "S" when shear failure would occur. TheMohr circle range is from the minimum normal effective stress (subscript 3) to the maximum (subscript 1).

Shear failure may be accompanied by irreversible mechanical changes, including activating old fractures,forming new ones, as well as wave propagation, ground motion, and even earthquakes (Haring et al., 2008).The prediction of shear failure is simulated in our model; however, since our geomechanical formulationis based on an elastic medium, the simulation of these irreversible mechanical changes is beyond the scopeof it.

Simulation ExamplesWe show simulation examples for code verification and demonstration of simulator capabilities. The firstexample is a simulation of caprock leakage resulting from carbon dioxide injection. This example is fromthe literature and we match some simulation results and demonstrate the simulator's prediction of shearfailure. We then run a variant of that problem where we simulate normal effective stress dependence offracture permeability and porosity. Finally, we simulate an experiment of pressure-induced fracturing of aconcrete block that includes tensile failure.

CO2 Leakage through Fault ZonesRinaldi at al. (2014) studied fault responses during underground carbon dioxide injection, and focusedon the short-term integrity of the sealing caprock and the potential for leakage. They considered stress/strain-dependent permeability and studied leakage through a fault zone as its permeability changes duringreactivation. We ran some of their simulations using our model. Their "Scenario 1" (Mazzoldi et al., 2012)was a two-dimensional system with a minor 1 km fault that intersected a 100 m thick injection aquiferbounded above and below by a 150 m thick low-permeability caprock, shown in Figure 2, with rockproperties shown in Table 1. Permeability and porosity depend on effective stress and is given by (Rutqvistand Tsang, 2002; Davies and Davies, 2001):

(25)

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(26)

where ϕ0 is zero effective stress porosity, ϕ1 is high effective stress porosity, exponent a is a parameter,constrant c is a parameter, and k0 is zero effective stress permeability.

Figure 2—Schematic of "Scenario 1," adapted from Rinaldi et al. (2014),showing rock layers and fault. Injection site starred point at 1500 m depth.

Table 1—Rock properties used aquifer-caprock system.

Property\Layer Upper Caprock CO2 reservoir Basal Fault

Young's modulus, GPa 10.0 10.0 10.0 10.0 5.0

Poisson's ratio 0.25 0.25 0.25 0.25 0.25

Porosity 0.10 0.01 0.10 0.01 0.10

Permeability, m2 10−14 10−19 10−13 10−16 10−14-10−16

Residual CO2 saturation 0.05 0.05 0.05 0.05 0.05

Residual liquid saturation 0.3 0.3 0.3 0.3 0.3

Van Genuchten (1980) p0,kPa 19.9 621 19.9 621 19.9

Van Genuchten (1980) m 0.457 0.457 0.457 0.457 0.457

We simulated this system using a 190x145 grid. Grid block x-direction length was 20 m, except for thex-direction interval the fault was located in where it was 2 m. Grid block y-direction length was 20 m,

SPE-182605-MS 9

except for the CO2 reservoir and caprock layers where it was 10 m. The fault was represented by a seriesof connected grid blocks that approximate lie on the fault line shown in Figure 2. We ran two cases, thefirst with fault permeability 10−14 m2 and CO2 injection rate of 0.10 kg/sec-m, and the second with faultpermeability 10−16 m2 and CO2 injection rate of 0.02 kg/sec-m, for five years. Figures 3 and 4 compareour fault permeability change at one and five years to those from the reference. There is good qualitativeagreement between the two.

Figure 3—Fault permeability increase for our simulation (a) and reference(b) for fault permeability of 10−14 m2 and CO2 injection rate of 0.10 kg/sec-m.

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Figure 4—Fault permeability increase for our simulation (a) and reference(b) for fault permeability of 10−16 m2 and CO2 injection rate of 0.02 kg/sec-m.

We also ran this simulation with a Mohr-Coulomb failure envelope to demonstate that capability of thesimulator to predict where shear failure of the fault could occur. The cohesion was zero and the coefficientof internal friction was 0.6. Figure 5 shows the predicted failure regions at varying times. These regionsonly lie along the fault; those outside the fault are not subject to shear failure.

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Figure 5—Mohr-Coulomb failure regions in fault shown at varying times: a) 544Ksec, b) 886 Ksec, c) 2851 Ksec, d) 11692 Ksec.

We ran a variant of this problem to demonstrate the calculation of permeability and porosity as a functionof normal stress for a fractured medium (Equations 20-22). The previous fault was changed to a verticalone located at x-direction 500 m and whose z-direction range is from 1000 to 2000 m, and represented bya column of grid blocks. The fault permeability in the z-direction depends on normal stress and since thefault is vertical, it depends on the normal x-direction stress component. Fault permeability in the x-directiondoes not change. We reran the case with fault permeability 10−14 m2 and CO2 injection rate of 0.10 kg/sec-m for five years. Figure 6 shows the gas saturation at 1- and 5-years and Figure 7 shows the permeabilityincrease at those times.

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Figure 6—Gas saturation at one and five years. The white lines denote the boundariesbetween rock regions and the 1 km fracture, located at x=500m, is centered at z=1500m.

Figure 7—Permeability ratio at one and five years. The white lines denote the boundariesbetween rock regions and the 1 km fracture, located at x=500m, is centered at z=1500m.

Fracture of a Concrete BlockIn order to develop a fundamental understanding of CO2 injection pressure-induced fracturing, we aredoing laboratory studies using concrete representations of caprock to determine the correlations betweenconfining stress, fluid pressure and fracturing initialization during CO2 injection. The equipment used forconducting these experiments includes a tri-axial loading system, an injection pump, and data acquisitiondevices. Initially, we use injected brine to identify the critical stress needed to initiate fractures in thesecaprock representations, which are 8 inch cubes that are cored in the center to create a 6 inch bore hole.We simulate one of these experiments, called "Sample 39" (Wu and Winterfeld, 2016). The cube initiallycontains a gaseous phase and its properties are shown in Table 2. The bore hole is simulated as a porousmedium with much higher permeability than the surrounding concrete.

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Table 2—Properties for brine injection experiment.

Concrete Bore hole

Young's modulus, GPa 6.0 6.0

Poisson's ratio 0.2 0.2

Porosity 0.10 0.90

Permeability, m2 1.0·10−15 1.0·10−14

Biot's coefficient 1.0 0.0

Tensile strength, MPa 2.0 —

Toughness, MPa 0.1 —

Fracture extension A, m/sec 10.0 —

Fracture extension n 1.0 —

The confining stresses are 1000 psi in x-direction, 1500 psi in y-direction, and 2000 psi in z-direction.The lateral boundaries are at constant pressure and brine is injected at 40 ml/min uniformly along the lowerhalf of the bore hole. The 11x11x11 grid is uniform in size. Since the minimum confining stress is in the x-direction, the concrete block will fracture in the yz-plane that contains the bore hole. We allow fracturingto occur only in that plane, which has the x-direction index of 6 in the grid. Figure 8 shows the simulatedfracture at a time of 531 seconds. The fracture is initiated along the bore hole and extends outward. Afterthe experiment is completed, the concrete block is dyed and broken apart by nitrogen in order to reveal thefracture induced by fluid injection. Figure 9 shows the result of this. The fracture is shown by the darker zonethat extends a distance from the bore hole. The simulated fracture is somewhat similar to the experimentin that the overall fracture extents are similar. The simulation is a highly idealized representation of thisprocess and is not expected to match the experiment in detail. For example, the fracture obtained by theexperiment is not symmetrical about the bore hole whereas the simulation must be due to the nature of thedata input (constant rock properties, and symmetry about the bore hole).

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Figure 8—Simulated fracture of concrete block. White indicates fracture, bore holeis in yellow and blue, with yellow the perforated region and blue unperforated.

Figure 9—Internal fracture morphology of concrete sample after dyeing and gas breakdown.

SPE-182605-MS 15

Summary and ConclusionsWe developed a thermal-hydrological-mechanical (THM) reservoir simulator that is applicable to assessingthe sealing capability of caprock. The geomechanical portion consists of an equation for mean stress, derivedfrom linear elastic theory for a thermo-poro-elastic system, and equations for stress tensor components thatdepend on mean stress and other variables. The fluid and heat flow portion of our simulator is for generalmultiphase, multicomponent, multi-porosity systems. We added the capability of simulating caprock failurescenarios, namely tensile failure, fracture and fault reactivation, and shear failure, to the formulation.

We verified our code by simulating of caprock leakage from carbon dioxide injection and matchingpublished results. In addition, we demonstrated its capabilities by simulating shear failure, the normaleffective stress dependence of fracture permeability and porosity, and an experiment of pressure-inducedfracturing of a concrete block that includes tensile failure.

AcknowledgementThis work was supported by the Foundation CMG, the EMG of the Colorado School of Mines, and by theNational Energy Technology Laboratory of the U. S. Department of Energy.

Nomenclaturea= parameterA= area, L2, m2

b = fracture aperture, mc = parameterC= fracture propagation velocity parameter, L/t, m/s

C0 = cohesion, m/Lt2, PaFb = body force, mL/t2, kg-m/s2

G = shear modulus, m/Lt2, Pahfr = fracture half height, m

I = identity matrixk = permeability, L2, m2

K = bulk modulus, m/Lt2, PaKI = stress intensity factor, m/Lt2, Pa

KIC = toughness, m/Lt2, Pan = fracture propagation velocity parameterP = pressure, m/Lt2, PaT = temperature, T, K

Tref = reference temperature, T, Ku = displacement vector, L, mv = velocity, L/t, m/sV = volume, L3, m3

wfr = fracture width, m

Greekα = Biot's coefficientβ = linear thermal expansion coefficient, 1/T, 1/Kε = strain tensorεv = volumetric strain

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λ = Lamé parameter, m/Lt2, Paμ = coefficient of internal frictionv = Poisson's ratio

σ1 = maximum principal stress, m/Lt2, Paσ3 = minimum principal stress, m/Lt2, Paσtn = tensile strength, m/Lt2, Paσ’ = effective stress, m/Lt2, Paτ = stress tensor, m/Lt2, Pa

τm = mean stress, m/Lt2, Paτ = shear stress, m/Lt2, Paϕ = porosityω = volume fraction

Subscriptsfr = fracturem = matrix0 = reference

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